Containing the Islamic State (ISIS) may be a more realistic strategy than defeating it, a committee of British lawmakers said, calling on Britain to play a greater role in the fight against the militants in Iraq and Syria.

Britain has so far taken part in U.S.-led air strikes against the Islamist group in Iraq, but not Syria. It has also provided some equipment and training for Kurdish forces.

Parliament's defence committee said in a report released on Thursday that these actions were "strikingly modest", with on average less than one air strike a day, and said it was "surprised and deeply concerned" Britain was not doing more.

The Iraqi security forces are weak and lack resources, the committee said, while the country's communities are divided and regional powers remain deeply suspicious of each other.

"There is a significant gap between the rhetoric of Britain and its partners, and the reality of the campaign on the ground ... It will be very difficult to destroy DAESH," the report said, using an Arabic acronym for the Islamic State.

"Given the deep polarisation and structural weaknesses of the Iraqi state, we wonder whether containment and suppression of DAESH would not be a more realistic goal than total elimination."

Islamic State is a breakaway al Qaeda group that declared an Islamic caliphate across parts of Syria and Iraq last summer. It has killed thousands in what the United Nations has called a reign of terror. On Tuesday, the group released a video showing a captured Jordanian pilot being burned alive.

The committee said that it was not calling for combat troops to be deployed, a move the government has ruled out, but said Britain should meet a request from the Iraqi army to provide training to counter Improvised Explosive Devices and also help with mission planning and tactics.

It also criticised ministers and military chiefs for failing to provide a clear idea of Britain's objectives or strategy in Iraq and called on the government to "radically" increase its defence and diplomatic engagement with regional powers such as Turkey and Saudi Arabia.

"We must clearly acknowledge the previous failures in Iraq, and reform our approach. But that does not mean lurching to doing nothing," said committee chairman Rory Stewart, a lawmaker from Prime Minister David Cameron's Conservative Party.

"There are dozens of things the UK could be doing ... to work with coalition partners to help address one of the most extreme threats that we have faced in the last 20 years."